Name one system where the compressional and tentional modulus of elesticity are different. Give reason
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Answer:
The compressive modulus of a material gives the ratio of the compressive stress applied to a material compared to the resulting compression, essentially how easy it is to squash the material between thumb and finger or in a vice.
The compressive strength gives the stress that is needed to destroy the sample by crushing. There is a complication though. If the material is brittle, such as concrete then the point of failure is clear. The sample suddenly fractures, frequently quite explosively as the stored energy is released. However if the material is ductile then it will slowly distort (this is called barrelling) and there is no single clear point of failure. An arbitrary line has to be drawn for the maximum permanent distortion that can be accepted.
The tensile strength of a material is the stress required to destroy that sample by tension. As with compressive stresses there will be a clear failure point if the material is brittle. Ductile materials however have several significant points:
- The limit of proportionality, beyond which the sample no longer obeys Hooke’s Law.
- The elastic limit, beyond which the sample will be permanently distorted.
- The yield stress beyond which there is a significant increase in the ease of distortion.
- The ultimate tensile stress, which is the largest stress that the sample can withstand, and the breaking stress at which the two ends of the sample are separated.
- The compressive stress of a ductile material best corresponds to the yield stress. Where no clear yield point exists then an arbitrary level of strain is agreed upon.
For both ductile and brittle materials the compressive strength is usually significantly higher than the tensile strength. An exception to this are the fibre reinforced composites such as fibre glass which are strong in tension but are easily crushed. Concrete however, which is a particle reinforced composite, is far stronger in compression than tension to the extent that if it is going to be exposed to tensile forces it needs to be reinforce with steel rods.
In conclusion compressive modulus and tensile modulus are the same only for steel or metal materials. But are not the same for brittle material as concrete.
Explanation:
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